function [A, B, D] = laminate_stiffness(layup, E1, E2, nu12, G12, G13, G23, varargin) % layup: Nx2 matrix [angle_deg, thickness_mm] nLayers = size(layup,1); A = zeros(3,3); B = zeros(3,3); D = zeros(3,3); z_top = 0; thickness = layup(:,2)*1e-3; total_h = sum(thickness); z_bottom = -total_h/2; for k = 1:nLayers theta = layup(k,1); zk = z_bottom + sum(thickness(1:k)); zk_prev = zk - thickness(k); % Compute Qbar for this layer Q = orthotropic_Q(E1, E2, nu12, G12); T = transformation_matrix(theta); Qbar = T * Q * T'; % Integrate A = A + Qbar * (zk - zk_prev); B = B + Qbar * 0.5 * (zk^2 - zk_prev^2); D = D + Qbar * (1/3) * (zk^3 - zk_prev^3); end end
% Transformation Matrix [T] T = [m^2, n^2, 2*m*n; n^2, m^2, -2*m*n; -m*n, m*n, (m^2-n^2)]; Composite Plate Bending Analysis With Matlab Code
the 2 by 1 column matrix; Row 1: the set cap N end-set, Row 2: the set cap M end-set end-matrix; equals the 2 by 2 matrix; Row 1: Column 1: open bracket cap A close bracket, Column 2: open bracket cap B close bracket; Row 2: Column 1: open bracket cap B close bracket, Column 2: open bracket cap D close bracket end-matrix; the 2 by 1 column matrix; Row 1: the set epsilon to the 0 power end-set, Row 2: the set kappa end-set end-matrix; (Extensional Stiffness): (Coupling Stiffness): (Bending Stiffness): is the vertical position of the k raised to the t h power layer relative to the mid-plane. SCIRP Open Access 5. Solve for Deformations and Stresses function [A, B, D] = laminate_stiffness(layup, E1, E2,
) using numerical methods like the .